p17p35ujimn9ejc9cap81i1j7e4.pdf

D GENERALIZATIONS ABOUT CRYSTAL STRUCTURES BASED ON PERIODICITY
Table 1.6. A test of the radius ratio rules for binary 1:1 compounds
compound r r r /r predicted CN observed CN
CsCl 1.67 1.81 0.92 8 8
CsBr 1.67 1.95 0.86 8 8
RbCl 1.48 1.81 0.82 8 6
TlBr 1.15 1.95 0.59 6 8
TlI 1.15 2.16 0.53 6 8
KI 1.33 2.16 0.62 6 6
MgO 0.82 1.76 0.46 6 6
MnO 0.75 1.76 0.43 6 6
CoO 0.72 1.76 0.41 6 6
NiO 0.69 1.76 0.39 4 6
ZnO 0.88 1.76 0.50 6 4
CdO 1.14 1.76 0.65 6 6
ZnS 0.88 2.19 0.40 4 4
ZnSe 0.88 2.38 0.37 4 4
Carefully chosen examples can make the radius ratio concept look like an
accurate predictive tool. However, it is often in error, particularly in complex
structures and when the bonding becomes increasingly covalent (where the hard
sphere model breaks down). Pauling [9] originally used the univalent radii (rather
than crystal radii) to calculate the radius ratio. A table of these values, together
with the crystal radii, can be found in Appendix 1A. However, the success rate
of the predictions does not depend strongly on which set of radii are used, as
long as both the cation and anion radii come from a set that was derived using
consistent assumptions. Examples of accurate and inaccurate predictions are
shown in Table 1.6 (calculated using Pauling’s univalent radii). Important
reasons for the inadequacy of this theory are the assumption of spherically symmetric
forces and symmetric coordination, the assumption that atoms have the
same size in all chemical environments, and the underestimation of ‘like-atom’
repulsions.
iii. Orbital hybridization in covalent structures
In contrast to isotropically bound metallic and ionic systems, covalent bonding
is directional. When a covalent bond is formed, electron density is increased
along the line connecting two bonding atoms. Covalent structures are formed
from atoms that have both s and p valence electrons (in effect, those on the righthand
side of the periodic chart with relatively high electronegativities). The formation
of sp hybrid orbitals results in four equivalent sp 3 orbitals directed
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